# Properties

 Label 126.3.s Level $126$ Weight $3$ Character orbit 126.s Rep. character $\chi_{126}(53,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $2$ Sturm bound $72$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 126.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(126, [\chi])$$.

Total New Old
Modular forms 112 8 104
Cusp forms 80 8 72
Eisenstein series 32 0 32

## Trace form

 $$8 q + 8 q^{4} + 12 q^{7} + O(q^{10})$$ $$8 q + 8 q^{4} + 12 q^{7} + 16 q^{10} + 56 q^{13} - 16 q^{16} - 20 q^{19} + 32 q^{22} - 60 q^{25} - 48 q^{28} - 100 q^{31} + 32 q^{34} + 76 q^{37} - 32 q^{40} - 248 q^{43} - 112 q^{46} + 44 q^{49} + 56 q^{52} + 176 q^{55} + 160 q^{58} - 64 q^{61} - 64 q^{64} + 108 q^{67} - 160 q^{70} + 60 q^{73} - 80 q^{76} - 364 q^{79} + 96 q^{82} + 224 q^{85} + 32 q^{88} + 404 q^{91} + 192 q^{94} + 480 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(126, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.s.a $4$ $3.433$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-14$$ $$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}+(-7+\cdots)q^{7}+\cdots$$
126.3.s.b $4$ $3.433$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$26$$ $$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{1}q^{5}+(5+3\beta _{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(126, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(126, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$